Mathematics and Statistics Vol. 1(3), pp. 102 - 112
DOI: 10.13189/ms.2013.010302
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Study of Nonlinear Evolution Equations to Construct Traveling Wave Solutions via the New Approach of the Generalized (G'/G) -Expansion Method

Md. Nur Alam^1,*, M. Ali Akbar², Harun-Or-Roshid ^1
1 Department of Mathematics, Pabna University of Science and Technology, Bangladesh
² Department of Applied Mathematics, University of Rajshahi, Bangladesh

ABSTRACT

Exact solutions of nonlinear evolution equations (NLEEs) play very important role to make known the inner mechanism of compound physical phenomena. In this paper, the new generalized (G'/G)-expansion method is used for constructing the new exact traveling wave solutions for some nonlinear evolution equations arising in mathematical physics namely, the (3+1)-dimensional Zakharov-Kuznetsov equation and the Burgers equation. As a result, the traveling wave solutions are expressed in terms of hyperbolic, trigonometric and rational functions. This method is very easy, direct, concise and simple to implement as compared with other existing methods. This method presents a wider applicability for handling nonlinear wave equations. Moreover, this procedure reduces the large volume of calculations.

KEYWORDS
The New Generalized (G'/G)-Expansion Method, the (3+1)-Dimensional Zakharov-Kuznetsov Equation and the Burgers Equation, Traveling Wave Solutions, Solitary Wave Solutions

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Md. Nur Alam , M. Ali Akbar , Harun-Or-Roshid , "Study of Nonlinear Evolution Equations to Construct Traveling Wave Solutions via the New Approach of the Generalized (G'/G) -Expansion Method," Mathematics and Statistics, Vol. 1, No. 3, pp. 102 - 112, 2013. DOI: 10.13189/ms.2013.010302.

(b). APA Format:
Md. Nur Alam , M. Ali Akbar , Harun-Or-Roshid (2013). Study of Nonlinear Evolution Equations to Construct Traveling Wave Solutions via the New Approach of the Generalized (G'/G) -Expansion Method. Mathematics and Statistics, 1(3), 102 - 112. DOI: 10.13189/ms.2013.010302.